NO
Non-Confluence Proof
Non-Confluence Proof
by Hakusan
Input
The rewrite relation of the following TRS is considered.
|
+(0,0) |
→ |
0 |
|
+(s(0),y) |
→ |
s(+(0,y)) |
|
+(x,s(y)) |
→ |
s(+(y,x)) |
|
s(s(x)) |
→ |
x |
Proof
1 Non-Joinable Fork
The system is not confluent due to the following forking derivations.
| t0
|
= |
+(y1,s(s(x1))) |
|
→2
|
+(y1,x1) |
|
= |
t1
|
| t0
|
= |
+(y1,s(s(x1))) |
|
→ε
|
s(+(s(x1),y1)) |
|
= |
t1
|
The two resulting terms cannot be joined for the following reason:
- When applying the cap-function on both terms (where variables may be treated like constants)
then the resulting terms do not unify.
Tool configuration
Hakusan